US10458937B2ActiveUtilityPatentIndex 58
Electromagnetic detector for detection of interface cracks in a piezoelectric-piezomagnetic laminated structure
Est. expiryMar 8, 2038(~11.7 yrs left)· nominal 20-yr term from priority
G01N 27/02G01R 29/22G01R 27/2611G01N 27/902
58
PatentIndex Score
1
Cited by
3
References
8
Claims
Abstract
The present invention discloses an electromagnetic detector and a detection method for detection of interface cracks in a piezoelectric-piezomagnetic laminated structure. The electromagnetic detector for detection of interface crack in a piezoelectric-piezomagnetic laminated structure mainly comprises an eddy current magnetic probe assembly, an automatic scanning frame, a base, a carrier, a servomotor, an X-axis mobile frame driving controller, a Y-axis mobile frame driving controller, a power supply, and a main controller.
Claims
exact text as granted — not AI-modifiedWe claim:
1. An electromagnetic detector for detection of an interface crack in a piezoelectric-piezomagnetic laminated structure, comprising an eddy current magnetic probe assembly ( 1 ), an automatic scanning frame ( 2 ), a base ( 3 ), a carrier ( 4 ), a servomotor ( 5 ), an X-axis movable frame driving controller ( 6 ), a Y-axis movable frame driving controller ( 7 ), a power supply ( 8 ), and a main controller ( 9 );
the carrier ( 4 ) is located on the base ( 3 ) with a permanent magnet ( 10 ) arranged between the carrier ( 4 ) and the base ( 3 ), the automatic scanning frame ( 2 ) is located above the carrier ( 4 ), the power supply ( 8 ) is configured to supply power for the servo motor ( 5 );
the automatic scanning frame ( 2 ) is provided on the upper part with a guide rail I ( 11 ), a guide rail II ( 12 ), an X-axis movable frame ( 13 ) and a Y-axis movable frame ( 14 );
the servo motor ( 5 ) is connected to the X-axis movable frame ( 13 ) and the Y-axis movable frame ( 14 ) via the X-axis movable frame driving controller and the Y-axis movable frame driving controller, respectively;
each of the guide rails 1 ( 11 ) and the guide rails II ( 12 ) is arranged in two, with two guide rails I ( 11 ) are arranged respectively on two long sides of the automatic scanning frame ( 2 ), and two guide rails II ( 12 ) are respectively arranged on two short sides of the automatic scanning frame ( 2 ), the X-axis movable frame ( 13 ) is arranged perpendicular to the guide rails II ( 12 ) and two ends of the X-axis movable frame ( 13 ) are installed on the two guide rails II ( 12 ) respectively,
the Y-axis movable frames ( 14 ) are in two, each of which is arranged perpendicular to the X-axis movable frame ( 13 ), and two ends of the two Y-axis movable frames ( 14 ) are installed on the two guide rails I ( 12 ) respectively,
the eddy current magnetic probe assembly ( 1 ) is arranged at the intersection of the X-axis movable frame ( 13 ) and one of the Y-axis movable frames ( 14 ) and is movable as the X-axis movable frame ( 13 ) and Y-axis movable frames ( 14 ) move,
a high-speed CCD camera ( 15 ) is arranged at the intersection of the X-axis movable frame ( 13 ) and the other Y-axis movable frame ( 14 ),
the eddy current magnetic probe assembly ( 1 ) and the high-speed CCD camera ( 15 ) are both connected to the main controller ( 9 ),
the main controller ( 9 ) is communicatively connected to a computer host ( 17 ),
the main controller comprises a magnetic signal extraction unit ( 18 ), a magnetic signal processing unit ( 19 ), a magnetic signal output unit ( 20 ), an image extraction unit ( 21 ), an image processing unit ( 22 ), a two-dimensional image generating unit ( 23 ), and an image signal output unit ( 24 ),
the magnetic signal extraction unit ( 18 ) is connected with the eddy current magnetic probe assembly ( 1 ) through a lead wire,
the image extraction unit ( 22 ) is connected to a high-speed CCD camera ( 15 ) through a lead wire,
the magnetic signal processing unit ( 19 ) is configured to receive and process the magnetic information extracted by the magnetic signal extraction unit and then send the processed data to the host computer ( 17 ) through the magnetic signal output unit ( 20 );
the image processing unit ( 22 ) is configured to receive and process the image information extracted by the image extraction unit ( 21 ), and then transmit the processed image information to the two-dimensional image generation unit ( 23 ) to generate a two-dimensional image of a structure and send data of the two-dimensional image to the computer host ( 17 ) through the image signal output unit ( 24 ),
a stress extraction sensor, an electric displacement sensor and a magnetic induction intensity sensor are all connected with the computer host ( 17 ) through the sensor control unit ( 16 ).
2. A method of detecting an interface crack in a piezoelectric-piezomagnetic laminated structure using the electromagnetic detector according to claim 1 , comprising the steps of:
(1) detecting the structure by the electromagnetic detector to, detect the position and the size of the crack, and storing the detected data result in a computer;
(2) establishing a two-dimensional model of the structure by a two-dimensional software in the computer, importing the generated two-dimensional model into finite element analysis software ANSYS 16.0 to establish a two-dimensional finite element analysis model of the structure, generating finite element mesh and inputting the crack data result detected in step (1) to determine the existence of a unit mesh with the crack;
(3) determining unit types, enrichment nodes and enrichment manner using level set function according to the finite element analysis model established by ANSYS 16.0 in step (2) and its mesh generation;
(4) introducing the step function reflecting discontinuous generalized displacements, and deducing the crack tip enrichment function which reflects the singularity of the generalized stress at the crack tip according to the crack tip asymptotic field of interface crack of piezoelectric-piezomagnetic laminated structure, such that a generalized displacement pattern is configured;
(5) deducing governing equations of mutual coupling of the magnetic, electrical and mechanical fields by using the principle of virtual work, combined with the above-mentioned extended finite element displacement model, and subjecting to discretization to obtain finite element equations of stiffness matrix and generalized force vector;
(6) calculating unit mass and stiffness matrix, dividing the units with discontinuous displacement and units with crack tip into several sub-regions to integrate using the high-order Gauss integral rule, and setting into global stiffness matrix;
(7) applying equivalent node loads and boundary conditions to solve the corresponding displacements, potentials and magnetic potentials and their derivatives, and further to obtain the corresponding stress, electrical displacement and magnetic induction intensity;
(8) calculating the total energy release rate using equivalent area integral of path-independent J-integral by the obtained stress, electrical displacement and magnetic induction intensity; obtaining the stress, electrical displacement and magnetic induction intensity factor using the interaction integral technique, and storing the resulting data in a computer storage medium.
3. The detection method according to claim 2 , wherein
in said step (2), said generating finite element mesh, is specifically:
firstly, establishing a two-dimensional model of the structure containing interface crack by the two-dimensional software in the computer, importing the generated two-dimensional model into finite element analysis software ANSYS 16.0 to, transform the two-dimensional model of the structure containing interface crack into a geometric shape finite element model of the structure containing interface crack,
then generating finite element mesh in the model by using the four-node quadrilateral unit, and numbering the unit as A1, A2, . . . An,
where n is the total number of generated units,
there are m units with cracks among said n units, and p units with crack tips, and all of the m, n and p are natural numbers,
as mesh generation is finished, the unit numbers of all the units, the unit node numbers and the coordinates of each node are output by the finite element software for subsequent calculation.
4. The detection method according to claim 2 , wherein
said determining unit types, enrichment nodes and enrichment manner using level set function, is specifically:
for the structure containing an interface crack, two horizontal set functions perpendicular to each other are required to describe the crack, that is, the normal level set function ζ (x, y) and the tangential level set function η (x, y), both of which are symbol distance functions;
for the cracks with two tips, two sets of tangential level functions η1 and η2 are defined, and a single level set function is defined according to the law of η=max (φ1, φ 2 ) on this basis,
with the above conditions, the crack is expressed by the level set functions ζ and η, that is, when η=0 and ζ=0, the crack is the tip, and the unit node at the tip should be enriched by a crack tip enrichment function. When η≤0 and ζ=0, the crack is the facial crack, and the nodes propagated by the facial crack should be enriched by a unit step function.
5. The detection method according to claim 2 , wherein the displacement mode is:
equation
(
1
)
u
h
(
x
)
=
∑
i
∈
N
N
i
(
x
)
u
i
+
∑
j
∈
N
H
N
j
(
x
)
[
H
(
f
(
x
)
)
-
H
(
f
(
x
j
)
)
]
a
j
+
∑
k
∈
N
Cf
N
k
(
x
)
∑
a
[
F
a
(
x
)
-
F
a
(
x
k
)
]
b
k
a
,
where i is a set of all unit nodes and j is a set of nodes of fully propagation unit, k is a set of nodes of the crack tip units;
Ni is a shape function of the corresponding unit node,
u i =[u i , v i , ϕ i , φ i ] T is a displacement vector of the unit node, ϕ and φ is a potential and a magnetic potential, respectively, a j , b k α is a displacement vector of the virtual node related to the step function H(x) and the facial crack enrichment function F α (x), respectively, for the problem of interface crack of the transversely isotropic piezoelectric piezomagnetic laminated structure, this enrichment function is derived in equation (2) as follows:
F ϕ ( r ,θ)=[ F 1 ϕ ( r ,θ), F 2 ϕ ( r ,θ), F 3 ϕ ( r ,θ), F 4 ϕ ( r ,θ)] Equation (2)
where (r,θ) is the polar coordinate system with the crack tip as the coordinate origin,
the superscript ϕ is used to distinguish the piezoelectric layer from the piezomagnetic layer, that is, when ϕ=e, the piezoelectric material is described, while when ϕ=m, the piezomagnetic material is described,
at the same time, each component in equation (2) is expressed as follows:
Equation ( 3 ) F s Φ ( r , θ ) = r β s Φ [ F s 1 Φ ( r , θ ) , F s 2 Φ ( r , θ ) , F s 3 Φ ( r , θ ) , F s 4 Φ ( r , θ ) , F s 5 Φ ( r , θ ) , F s 6 Φ ( r , θ ) ] T F x1 ϕ ( r ,θ)= e −εψ ϕ ,cos ∂ s ϕ ,F s2 ϕ ( r ,θ)= e −εψ ϕ ,sin ∂ s ϕ ,F s3 ϕ ( r ,θ)= e εψ ϕ ,cos χ s ϕ F s4 ϕ ( r ,θ)= e εψ ϕ ,sin χ s (m) ,F s5 ν ( r ,θ)=cos(ψ s ϕ /2), F s6 ϕ ( r ,θ)=sin(ψ s ϕ /2) Equation (4)
Equation
(
5
)
β
s
Φ
=
[
cos
θ
+
Re
(
p
s
Φ
)
sin
θ
]
2
+
[
Im
(
p
s
Φ
)
sin
θ
]
2
ψ
s
Φ
=
arg
[
cos
θ
+
p
s
Φ
sin
θ
]
,
ϑ
s
Φ
=
ɛ
ln
(
r
β
s
Φ
)
+
ψ
s
Φ
/
2
χ
s
Φ
=
ɛ
ln
(
r
β
s
Φ
)
-
ψ
s
Φ
/
2
for all the above equations s=1, 2, 3, or 4;
ε is the singularity oscillation factor of the crack tip whose value is only related to the material constants and the way that structures combined; and
ps is the four feature values obtained by governing the equations.
6. The detection method according to claim 2 , wherein the control equation in which the piezoelectric material and the piezomagnetic material are coupled to each other is as shown in Equation (6)
Equation
(
6
)
{
(
c
ijks
e
ɛ
ks
e
-
e
sij
e
E
s
e
)
.
j
=
0
,
(
e
iks
e
ɛ
ks
e
+
α
is
e
E
s
e
)
.
i
=
0
,
(
μ
is
e
H
s
e
)
.
i
=
0
,
{
c
ijks
m
ɛ
ks
m
-
h
sij
m
H
s
M
)
.
j
=
0
,
(
α
is
m
E
s
m
)
.
i
=
0
,
(
h
iks
m
ɛ
ks
m
+
μ
is
m
H
s
m
)
.
i
=
0
,
(
6
)
Where ε ij ϕ , E i ϕ , H i ϕ are stress, electric field and magnetic field, respectively;
c ijks ϕ , e iks ϕ , h iks ϕ , α is ϕ and μ is ϕ are elastic constants, piezoelectric constant, piezomagnetic constant, dielectric constant, and permeability rate, respectively.
7. The detection method according to claim 2 , wherein the stiffness matrix and generalized force vector obtained by substituting the above extended finite element displacement model into the governing equation to discretize using the principle of virtual work is:
Ku h =f, Equation (7)
where K and f are global stiffness matrix and node force vector, respectively, which are composed of the unit stiffness matrix and the node force vector set, respectively, and for each unit, its unit mass matrix and stiffness matrix and node force vector are expressed as:
Equation
(
8
)
k
ij
e
=
[
k
ij
uu
k
ij
ua
k
ij
ub
k
ij
a
u
k
ij
aa
k
ij
ab
k
ij
bu
k
ij
ba
k
ij
bb
]
,
f
i
e
=
{
f
i
u
f
i
a
f
i
b
1
f
i
b
2
L
L
f
i
b
l
}
T
,
where u, a and b correspond to the generalized displacement vector and the generalized degree of freedom vector corresponding to the enrichment function, I is the number of crack tip enrichment function, and
Equation
(
9
)
k
ij
ls
=
∫
Ω
c
(
B
i
l
)
T
C
(
B
j
s
)
d
Ω
,
(
t
,
s
=
u
,
a
,
b
α
)
,
f
i
l
=
∫
∂
Ω
c
S
i
l
t
_
d
Γ
+
∫
Ω
c
S
i
l
f
_
d
Ω
,
(
t
=
u
,
a
,
b
α
)
,
in the above two equations,
Equation (10)
S i a =N i ,S i a =N i [ H ( f ( x ))− H ( f ( x i ))], S i b a =N i [ F α ( x )− F α ( x i )] (10)
C is elastic matrix of materials, t and f are the generalized surface forces and physical forces, respectively, F α is the first component of the enrichment function F, and the geometric matrix B i a , B i a and B i b and are expressed as:
Equation ( 11 ) B i u = [ N i , x 0 0 0 0 N i , y 0 0 N i , y N i , x 0 0 0 0 N i , x 0 0 0 N i , y 0 0 0 0 N i , x 0 0 0 N i , y ] ,
B i a = [ S i , x a 0 0 0 0 S i , y a 0 0 S i , y a S i , x a 0 0 0 0 S i , x a 0 0 0 S i , y a 0 0 0 0 S i , x a 0 0 0 S i , y a ] ,
B i b a = [ S i , x b a 0 0 0 0 S i , y b a 0 0 S i , y b a S i , x b a 0 0 0 0 S i , x b a 0 0 0 S i , y b a 0 0 0 0 S i , x b a 0 0 0 S i , y b a ] ,
B i b =[ B i b 1 B i b 2 L L B i b i ], Equation (12)
subjecting the equation (4) to process by introducing the boundary conditions, to solve the generalized displacement vector of the node, and further obtain the generalized stress vector of the node.
8. The detection method according to claim 2 , wherein the J integral is calculated by the following equivalent area integral:
Equation
(
13
)
J
=
∫
A
(
σ
ij
u
i
,
1
+
D
j
ϕ
.1
+
B
j
φ
.1
-
W
δ
1
j
)
q
.
j
d
A
+
∫
A
(
σ
ij
u
i
,
1
+
D
j
ϕ
.1
+
B
j
φ
.1
-
W
δ
1
j
)
.
j
qdA
,
i
,
j
=
1
,
3
,
where A is the area surrounded by the integrated contour with r as radius and the crack tip as the center, q is a weight function and is 1 in the area A, and 0 outside the area A, σ ij , D i , B i are stress, electric displacement, magnetic induction of each unit node, respectively,
Equation
(
14
)
W
=
1
2
(
σ
ij
ɛ
ij
-
D
j
E
j
-
B
j
H
j
)
,
i
,
j
=
1
,
3
,
J integral has the following relationship with stress, electric displacement and magnetic induction intensity factor:
J
=
1
4
K
T
UK
,
where U is a matrix formed by material constants:
K =[ K H K I K D K B ] T Equation (15)
for two independent equilibrium states: state 1 is the real state, state 2 is the auxiliary state, the interaction integral is:
2 M (1,2) =K H (1) K H (2) U 11 +K I (1) K I (2) U 22 +K D (1) K D (2) U 33 +K B (1) K B (2) U 44 +( K I (1) K H (2) +K H (1) K I (2) ) U 12 +( K H (1) K D (2) +K D (1) K H (2) ) U 13 +( K H (1) K H (2) +K B (1) K H (2) )+ U 14 +( K I (1) K D (2) +K D (1) K I (2) ) U 23 +( K I (1) K B (2) +K B (1) K I (2) ) U 24 +( K D (1) K B (2) +K B (1) K D (2) U 34 Equation (16)
in order to facilitate calculation, in the state (2), K I (2) =1 and K H (2) =K D (2) =K B (2) =0, and are substituted into the equation (7), to get that the generalized stress in the true state satisfy the following relationship:
2{ M (1,H) ,M (1,I) ,M (1,D) ,M (1,B) } T =U{K H (1) ,K I (1) ,K D (1) ,K B (1) } T Equation (17)
then solve it,
finally, the J integral and generalized stress intensity factor and other data are stored in the computer storage data.Cited by (0)
No later patents cite this yet.
References (0)
No backward citations on record.